Simple Harmonic Motion

Physics Laboratory Report Simple agreeable interrogative Determining the intensity level constant Aim of try out The objective of this audition is 1. To study the simple benevolent motion of a galvanic pile- ring system 2. To adjudicate the force constant of a terpsichore Principles involved A even or vertical troop- fountain system depose perform simple benevolent motion as shown below. If we know the purpose (T) of the motion and the press (m), the force constant (k) of the jump off can be narrow downd. pic Consider pulling the nap of a horizontal corporation- leap out system to an extension x on a table, the smoke subjected to a restoring force (F=-kx) stated by Hookes Law.If the mass is now released, it will move with acceleration (a) towards the equilibrium position. By newtons indorse law, the force (ma) acting on the mass is refer to the restoring force, i. e. ma = -kx a = -(k/m)x -(1) As the movement continues, it performs a simple harmonic motion with angular velocity (? ) and has acceleration (a = -? 2x). By comparing it with comparison (1), we have ? = v(k/m) Thus, the period can be represented as follows T = 2? /? T = 2? x v(m/k) T2 = (4? 2/k) m (2)From the comparability, it can be seen that the period of the simple harmonic motion is independent of the bountifulness. As the pass on also applies to vertical mass- pass over system, a vertical mass- chute system, which has a sm tout ensemble frictional effects, is used in this experiment. Apparatus Slotted mass (20g)x 9 Hanger (20g)x 1 Springx 1 Retort stand and clampx 1 Stop watchx 1 G-clampx 1 Procedure 1. The apparatuses were decorate up as shown on the right. 2. No slotted mass was originally locate into the hanger and it was set to oscillate in moderate amplitude. 3.The period (t1) for 20 complete bikes was measured and recorded. 4. Step 3 was repeated to beget a nonher record (t2). 5. Steps 2 to 4 were repeated by adding one slotted mass to the hanger from each one clipping until all of the nine accustomed masses have been used. 6. A graph of the square of the period (T2) against mass (m) was plotted. 7. A best-fitted line was drawn on the graph and its slope was measured. perplexity 1. The oscillations of the spring were of moderate amplitudes to reduce errors. 2. The oscillations of the spring were guardedly initiated so that the spring did not swing to ensure stainless results. . The spring used was carefully chosen that it could perform 20 oscillations with little decay in amplitude when the hanger was put on it, and it was not over-stretched when all the 9 slotted masses were put on it. This could ensure accurate and tried and true results. 4. The experiment was carried out in a place with little tonal pattern movement (wind), in secernate to reduce swinging of the spring during oscillations and errors of the experiment. 5. The spring was clamped tightly so that the spring did not slide during oscillation. It lessen energy lo ss from the spring and ensured accurate results. . A G-clamp was used to attach the stand firmly on the bench.This reduced energy loss from the spring and ensured accurate results. Results Hanger and slotted mass 20 periods / s One period (T) T2 / s2 (m) / kg / s t1 t2 Mean (0. 1s) (0. s) = (t1 + t2) / 2 0. 02 5. 0 5. 4 5. 2 0. 26 0. 0676 0. 04 6. 0 6. 0 6. 0 0. 3 0. 09 0. 06 7. 0 7. 0 7. 0 0. 35 0. 1225 0. 08 7. 8 7. 8 7. 8 0. 9 0. 1521 0. 10 8. 6 8. 6 8. 6 0. 43 0. 1849 0. 12 9. 4 9. 5 9. 45 0. 4725 0. 22325625 0. 14 10. 1 10. 1 10. 1 0. 505 0. 255025 0. 16 10. 5 10. 4 10. 45 0. 5225 0. 27300625 0. 8 11. 1 11. 3 11. 2 0. 56 0. 3136 0. 20 11. 9 12. 0 11. 95 0. 5975 0. 35700625 Calculations and recital of results pic From equation (2), the slope of the graph is equal to (4? 2/k), i. e. 1. 5968 = 4? 2/k k = 4? 2/1. 5968 ? 24. 723 Nm-1 ?The force constant of the spring is 24. 723 Nm-1. Sources of error 1. The spring swung during oscillations in the experiments. 2.As the amplitudes of oscillations were small, there was difficulty to determine whether an oscillation was completed. 3. Reaction time of restrainr was involved in time-taking. 4. Energy was deep in thought(p) from the oscillations of the spring to resonance of the spring. Order of Accuracy Absolute error in time-taking = 0. 1s Hanger and slotted mass (m) / kg 20 periods / s Relative error in time-taking t1 t2 (0. s) (0. 1s) t1 t2 0. 02 5. 0 5. 4 2. 00% 1. 85% 0. 04 6. 0 6. 0 1. 67% 1. 67% 0. 06 7. 0 7. 0 1. 3% 1. 43% 0. 08 7. 8 7. 8 1. 28% 1. 28% 0. 10 8. 6 8. 6 1. 16% 1. 16% 0. 12 9. 4 9. 5 1. 06% 1. 05% 0. 14 10. 1 10. 1 0. 990% 0. 990% 0. 6 10. 5 10. 4 0. 952% 0. 962% 0. 18 11. 1 11. 3 0. 901% 0. 885% 0. 20 11. 9 12. 0 0. 840% 0. 833% Improvement 1. The spring should be initiated to oscillate as vertical as possible to prevent swinging of the spring, which would cause energy loss from the spring and give inaccurate results. 2. some(prenominal) observers could observe the oscillations of the spring and determine a more(prenominal) accurate and reliable result that whether the spring has completed an oscillation. 3. The time taken for oscillations should be taken by the same observer. This allows more reliable results as error-error cancellation of reaction time of the observer occurs. 4. The spring used should be do of a material that its resonance frequency is difficult to match. Discussion In this experiment, several assumptions were made. First, it is assumed that the spring used is tipless and resonance does not occur.Furthermore, it is assumed that no energy is lost from the spring to overcome the air resistance. Besides, it is assumed that no swinging of the spring occurs during the experiment. In addition, there were difficulties in carrying out the experiment. For timing the oscillation, as the spring oscillates with moderate amplitude, it was hard to determine if a complete oscillation has been accomplished. Added to t his, in drawing the best-fitted line, as all the points do not join to form a straight line, there was a little difficult encountered while drawing the line.Nevertheless, they were all solved. Several observers observed the oscillations of the spring and determined a more reliable result that whether the spring has completed an oscillation. For the best-fitted line, computer was employed to obtain a reliable graph. Conclusion The mass-spring system performs simple harmonic motion and the force constant of the spring used in this experiment is 24. 723 Nm-1. A graph of T2 against m Square of the period (T2) picSimple Harmonic MotionShanise Hawes 04/04/2012 Simple Harmonic Motion Lab Introduction In this two part lab we sought out to demonstrate simple harmonic motion by observing the behavior of a spring. For the first part we needed to observe the motion or oscillation of a spring in aim to make up ones mind k, the spring constant which is commonly described as how implike the s pring is. Using the equation Fs=-kx or, Fs=mg=kx where Fs is the force of the spring, mg represents mass times gravity, and kx is the spring constant times the distance, we can mathematically keep apart for the spring constant k.We can also graph the data placid and the slope of the line will reflect the spring constant. In the routine part of the lab we used the equation T=2? mk, where T is the period of the spring. After calculating and graphing the data the x-intercept represented k, the spring constant. The spring constant is technically the measure of elasticity of the spring. Data mass of lading displacement m (kg) x (m) 0. 1 0. 12 0. 2 0. 24 0. 3 0. 36 0. 4 0. 48 0. 5 0. 60We began the experiment by placing a helical spring on a clamp, creating a spring system. We then measured the distance from the furnish of the suspend spring to the floor. bordering we placed a 100g tilt on the bottom of the spring and then measured the displacement of the spring due to the tilt . We repeated the procedure with 200g, 300g, 400g, and 500g weights. We then placed the recorded data for each trial into the equation Fs=mg=kx. For example 300g weight mg=kx 0. 30kg9. 8ms2=k0. 36m 0. 30kg 9. 8ms20. 36m=k 8. 17kgs=kHere we graphed our collected data. The slope of the line verified that the spring constant is just about 8. 17kgs. In the second part of the experiment we suspended a 100g weight from the bottom of the spring and pulled it very slightly in order to set the spring in motion. We then used a timer to time how long it took for the spring to make one complete oscillation. We repeated this for the 200g, 300g, 400g, and 500g weights. Next we divided the times by 30 in order to decide the average period of oscillation. We then used the equation T2=4? mk to mathematically isolate and notice k. Lastly we graphed our data in order to find the x-intercept which should represent the value of k. Data Collected Derived Data mass of weight time of 30 osscillation a vg osscilation T T2 m (kg) t (s) t30 (s) T2 s2 0. 10 26. 35 0. 88 0. 77 0. 20 33. 53 1. 12 1. 25 0. 30 39. 34 1. 31 1. 72 0. 40 44. 81 1. 49 2. 22 0. 50 49. 78 1. 66 2. 76 Going back to our equation T2=4? 2mk .We found the average period squared and the average mass and set the equation up as T2m=4? 2k. Since T2 is our change in y and m is our change in x, this also helped us to find the slope of our line. We got T2m equals approximately 4. 98s2kg. We now have 4. 98s2kg= 4? 2k. Rearranging we have k=4? 24. 98s2k= 7. 92N/m. Plotting the points and observing that the slope of our line is indeed approximately 4. 98 we see that the line does cross the x-axis at approximately 7. 92. Conclusion precedent to placing any additional weight onto our spring we measured the length of spring to be 0. 8m. So if we hooked an identical spring and an additional 200g the extension of our total spring would be approximately 0. 8m accounting for twice our spring and the . 24m the additional wei ght added. However, I intend the additional weight of the second spring would slightly elongate the initial spring bringing it nigh over a meter. Since our spring elongation has almost tripled I believe that an effective spring constant would be triple that of what we found it to be initially, making a new spring constant of 24. 51kgs